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RESEARCH ARTICLE

Modeling and analysis of the dynamics of an excessive gambling problem with modified fractional operator

Mulualem Aychluh1 ,  D.L. Suthar2,3* ,  Clemente Cesarano4 ,  S.D. Purohit5
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1 Department of Mathematics, Samara University, Samara, Afar, Ethiopia
2 Department of Mathematics, Wollo University, Dessie, Ethiopia
3 Department of Mathematics, Saveetha School of Engineering (SIMATS), Thandalam, Chennai, Tamil Nadu, India
4 International Telematic University UNINETTUNO, Roma, Italy
5 Rajasthan Technical University, Kota, Rajasthan, India
IJOCTA, 7096 https://doi.org/10.36922/ijocta.7096
Received: 6 December 2024 | Revised: 7 April 2025 | Accepted: 16 April 2025 | Published online: 5 May 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This work introduces a fractional-order model of gambling addiction using the modified Atangana-Baleanu-Caputo operator. We establish solution existence/uniqueness, derive the reproduction number R0, and analyze stability. Numerical results demonstrate how fractional order υ influences addiction dynamics. The model identifies key intervention parameters through sensitivity analysis. The optimal control strategy is proposed to reduce progression to addiction. These approaches provide new tools for understanding and managing problem gambling behaviors.

Keywords
Excessive gambling problem
Modified fractional operator
Numerical method
Fractional mathematical modeling
Funding
None.
Conflict of interest
The authors declare they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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